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integralBoxFilter

2-D box filtering of integral images

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Syntax

B = integralBoxFilter(A)
B = integralBoxFilter(A,filterSize)
B = integralBoxFilter(___,"NormalizationFactor",normFactor)

Description

B = integralBoxFilter(A) filters the integral image A with a 3-by-3 box filter. Returns the filtered image, B.

B = integralBoxFilter(A,filterSize) filters the integral image A with a 2-D box filter with size specified by filterSize.

example

B = integralBoxFilter(___,"NormalizationFactor",normFactor) also specifies the normalization factor applied to the box filter.

Examples

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Open Live Script

Read image into the workspace.

A = imread('cameraman.tif');

Pad the image by the radius of the filter neighborhood. This example uses an 11-by-11 filter.

filterSize = [11 11];
padSize = (filterSize-1)/2;
Apad = padarray(A, padSize, 'replicate','both');

Compute the integral image of the padded input image.

intA = integralImage(Apad);

Filter the integral image.

B = integralBoxFilter(intA, filterSize);

Display original image and filtered image.

figure
imshow(A)
title('Original Image')

Figure contains an axes object. The hidden axes object with title Original Image contains an object of type image.

figure
imshow(B,[])
title('Filtered Image')

Figure contains an axes object. The hidden axes object with title Filtered Image contains an object of type image.

Open Live Script

Read image into the workspace.

 A = imread('cameraman.tif');

Pad the image by radius of the filter neighborhood, calculated (11-1)/2.

padSize = [5 5]; 
Apad = padarray(A, padSize, 'replicate', 'both');

Calculate the integral image of the padded input.

intA = integralImage(Apad);

Filter the integral image with a vertical [11 1] filter.

Bvert = integralBoxFilter(intA, [11 1]);

Crop the output to retain input image size and display it.

Bvert = Bvert(:,6:end-5);

Filter the integral image with a horizontal [1 11] filter.

Bhorz = integralBoxFilter(intA, [1 11]);

Crop the output to retain input image size.

Bhorz = Bhorz(6:end-5,:);

Display the original image and the filtered images.

figure,
imshow(A)
title('Original Image')

Figure contains an axes object. The hidden axes object with title Original Image contains an object of type image.

figure,
imshow(Bvert,[])
title('Filtered with Vertical Filter')

Figure contains an axes object. The hidden axes object with title Filtered with Vertical Filter contains an object of type image.

figure,
imshow(Bhorz,[])
title('Filtered with Horizontal Filter')

Figure contains an axes object. The hidden axes object with title Filtered with Horizontal Filter contains an object of type image.

Input Arguments

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Integral image to be filtered, specified as a numeric array of any dimension.

The integral image must be upright — integralBoxFilter does not support rotated integral images. The first row and column of the integral image is assumed to be zero-padded, as returned by integralImage.

Data Types: double

Size of box filter, specified as a positive, odd integer or 2-element vector of positive, odd integers. If filterSize is scalar, then integralBoxFilter uses a square box filter.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Normalization factor applied to the box filter, specified as a numeric scalar.

By default, the normalization factor has the value 1/filterSize.^2 when filterSize is a scalar, and 1/prod(filterSize) when filterSize is a vector. The default has the effect of a mean filter — the pixels in the output image are the local means of the image.

To get local area sums, set normFactor to 1. To avoid overflow in such circumstances, consider using double precision images by converting the input image to data type double.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64

Output Arguments

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Filtered image, returned as a numeric array. integralBoxFilter returns only the parts of the filtering that are computed without padding.

Data Types: double

Extended Capabilities

Version History

Introduced in R2015b

See Also

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